Maybe I can explain a bit. Petrol has a low boiling point, (the temperature at which it turns to vapour), at normal ambient it's ok, but as temperature increases, it is more likely to boil/vaporise.
Putting petrol under pressure raises the boiling point, (like a pressure cooker). The logic in the FSI Fuel system is that in order to ensure the fuel doesn't vaporise before it gets to the high pressure pump inlet on a hot engine, the electric fuel pump runs at a higher pressure than normal, 5.8 Bar not the normal 4.0 Bar.
In
@VVVVVV car, the high pressure pump is working fine, once the engine is running, so it's probably OK. my guess is that the electric pump is not producing 5.8 Bar when the engine is hot, so the fuel supply to the high pressure pump is vaporising, and the ECU produces a low pressure DTC for the high pressure pump as a result of vapour at the inlet. Once the engine running, all is well, as cooler fresh fuel is drawn from the tank.
The electric pump is either faulty, or the fuel metering valve is not closing as it should for a hot start.
Mac.